If 400 bricks, each measuring 81" by 31", are required to build a wall 42 feet high, how long is the wall?
81 x 31 = 2 511 (area of a brick)
2511 x 400 = 1 004 400 (area of the wall)
Convert 1 004 400" to ft. [1ft. = 12"]
1 004 400 / 12 = 83 700 ft.
Now this is what we have.
-Hight 42 ft.
-Length X ft.
-Area 83 700ft.
Algebra time.
42 x X = 83 700 (to get X you would devide 83 700 by 42)
83 700 / 42 = 1 992.85ft. (X = 1 992.85ft.)
So the length of the wall would be 1992.85ft.
The height of the wall is 166.07 ft.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 400 bricks, each measuring 81" by 31", are required to build a wall 42 feet high.
Here, Area of a one brick 81"×31"
6.75×2.58=17.44 ft²
Total area of 400 bricks = 400×17.44=6975 ft²
Total brick area divided by 42' height of wall
=6975÷42=166.07 ft
Therefore, the height of the wall is 166.07 ft.
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Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A followed by a 2 from B?
The probability that a 4 is drawn from A followed by a 2 from B is 1/24
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
Urn A has balls numbered 1 through 6 → Total = 6 ballsThe probability of choosing a 4 ( 1 ball ) from Urn A is:
[tex]P(A) = \boxed{\frac{1}{6}}[/tex]
Urn B has balls numbered 1 through 4 → Total = 4 ballsThe probability of choosing a 2 ( 1 ball ) from Urn B is:
[tex]P(B) = \boxed {\frac{1}{4}}[/tex]
The probability that a 4 is drawn from A followed by a 2 from B is
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
[tex]P(A \cap B) = \frac{1}{6} \times \frac{1}{4}[/tex]
[tex]P(A \cap B) = \boxed {\frac{1}{24}}[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
The lines 2x - 3y = 1 and 2x + 3y = 2 are intersecting. true or false
Answer:
the given statement is true.
Step-by-step explanation:
The given lines are
2x - 3y = 1 and 2x + 3y = 2
Write these equations in slope intercept form of a line y = mx +b
For the first equation
[tex]2x-3y=1\\\\3y=2x-1\\\\y=\frac{2}{3}x-\frac{1}{3}[/tex]
For the first equation
[tex]2x+3y=2\\\\3y=-2x+2\\\\y=-\frac{2}{3}x+\frac{2}{3}[/tex]
The slope and y-intercepts of first line are 2/3 and -1/3 respectively.
The slope and y-intercepts of second line are -2/3 and 2/3 respectively.
Since, the slopes and y-intercepts of these lines are different.
Hence, these lines are intersecting.
Therefore, the given statement is true.
Paul and Scott were solving the same problem. Who is wrong? Explain their error.
Paul Scott
__________________
log 3x=9 log 3x=9
3^x=9 x=3^9
3^x=3^2 x=19,683
x=2
How are line graphs used to show how two variables are related?
Quadrilateral ABCD is an Isosceles Trapezoid. Which angle is congruent to Angle C?
Answer:
The reason why any angles coming out from D and C are congruents is because of the geometry coungruence's concept of 2 items having the same pattern, shape or form and size as the mirror image of the other.
2 angles would be congruent by being the same angle in degrees or radians.
Thereby any angle coming out from C as vertex would be congruent with any other vertex point angle mirroring the resulting figure shaped by the radiants or degrees of such angle.
Step-by-step explanation:
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h=-16t^2+36t+5. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height
1)1.13 s; 27.5 ft
2)2.25 s; 5 ft
3)1.13 s; 25.25 ft
4)1.13 s; 65.75 ft
Answer: 1.13s;25.25ft you welcome
Step-by-step explanation:
The total cost of a vacation to a rain forest includes a fee of $560 for the tour guide, plus $630 per person. The function y=560+630x/ x
models the average cost per person, in dollars, when x people go on the vacation.
What is the horizontal asymptote of the function?
y= ????
Answer: y= 630 is the horizontal asymptote for the given function.
Step-by-step explanation:
Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to [tex]+\infty[/tex] or [tex]-\infty[/tex].
Thus, If there is a function f(x),
Then Its horizontal asymptote, y = [tex]\lim_{x\rightarrow \infty} f(x)[/tex]
Here the given function is, [tex]f(x) = \frac{560+630x}{x}[/tex]
Thus its horizontal asysmptote is, y = [tex]\lim_{x\rightarrow \infty} \frac{560+630x}{x}[/tex]
⇒ y = [tex]\lim_{x\rightarrow \infty}560/x+630[/tex]
⇒ y = 0+ 630
⇒ y= 630 is the horizontal asymptote of the given function f(x).
The horizontal asymptote of y = (630x + 560)/x is y = 630.
Linear functionA linear function is given by:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Given the total cost as y = 630x + 560.
For the function y = (630x + 560)/x, the horizontal asymptote is at:
y = 630x/ x = 630
The horizontal asymptote of y = (630x + 560)/x is y = 630.
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Kieran’s wallet contains 7 bills: three $5 bills, two $10 bills, one $20 bill, and one $100 bill. if kieran pulls out two bills at random, what is the probability that he selects exactly two $5 bills?
Answer:
[tex]\bf\textbf{Probability of selecting exactly two $5 bill }=\frac{1}{7}[/tex]
Step-by-step explanation:
Total number of bills in the wallet = 7
Total number of $5 bills in the wallet = 3
Total number of $10 bills in the wallet = 2
Total number of $20 bill in the wallet = 1
Total number of $100 bill in the wallet = 1
We need to find the probability that he selects exactly two $5 bills.
Number of favorable outcomes = 3
[tex]\text{Probability of selecting one $5 bill }\frac{3}{7}[/tex]
[tex]\text{Probability of selecting second $5 bill }\frac{2}{6}[/tex]
[tex]\bf\textbf{Probability of selecting exactly two $5 bill = }\frac{3}{7}\times \frac{2}{6}=\frac{1}{7}[/tex]
Help! question down below!
they would be similar since they have the same angles, but different length sides
they are different sizes
the sides are different lengths
congruent, means same size and shape
the only answer that applies is A
PLEASE HELP!!!!!!!!!!!!! GEOMETRY
The following graph describes function 1, and the equation below it describes function 2:
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 15
Function ____ has the larger maximum.
(Put 1 or 2 in the blank space)
Answer:
The Function __1__ has the larger maximum.
Step-by-step explanation:
The given functions are
Function 1:
[tex]f(x)=-x^2+8x-15[/tex]
Function 2:
[tex]f(x)=-x^2+2x-15[/tex]
Both functions are downward parabola because the leading coefficient is negative. So, the vertex is the point of maxima.
If a function is [tex]f(x)=ax^2+bx+c[/tex], then its vertex is
[tex]Vertex=(\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]
The vertex of Function 1 is
[tex]Vertex=(\frac{-8}{2(-1)}, f(\frac{-8}{2(-1)}))[/tex]
[tex]Vertex=(4, f(4))[/tex]
The value of f(4) is
[tex]f(4)=-(4)^2+8(4)-15=1[/tex]
The vertex of Function 1 is (4,1). Therefore the maximum value of Function 1 is 1.
The vertex of Function 2 is
[tex]Vertex=(\frac{-2}{2(-1)}, f(\frac{-2}{2(-1)}))[/tex]
[tex]Vertex=(1, f(1))[/tex]
The value of f(1)is
[tex]f(1)=-(1)^2+2(1)-15=-14[/tex]
The vertex of Function 2 is (1,-14). Therefore the maximum value of Function 2 is -14.
Since 1>-14, therefore Function __1__ has the larger maximum.
Find the median of the following set of data. $12.50, $13.23, $11.20, $14.50, $12.50, $13.23, $15.60, $15.75
Answer:
The answer is 13.23
Step-by-step explanation:
In order to determine the median of the set of data, we have to know about median and how applicate it.
The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.
Also, if there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
So, we arrange the set of data:
11.20
12.50
12.50
13.23
13.23
14.50
15.60
15.75
The data set is an even number.
The two middlemost numbers are: 13.23; 13.23.
So, the mean (average) is:
(13.23+13.23)/2=13.23
Finally, the median of the set of data is 13.23
The area of a triangle is ½ (b) (h), where the base and height are always two sides of the triangle.
a. True
b. False
Which is the graph of f(x)=3/2(1/3)^x
Answer:
Graph B
Step-by-step explanation:
Given is a function as
[tex]f(x) = \frac{3}{2} (\frac{1}{3} )^x[/tex]
There are 4 graphs given.
Out of the 4 options we have to select one which suits this graph
Let us study about f graph
X intercept is at infinity.
Or y=0 is asymptote for this curve
y intercept is when x =0
i.e. y intercept =3/2 (1) = 3/2
Only A and B satisfy this value of y intercept
Out of A and B we have to select one option
When x=1, we get
f(1) = 3/2 (1/3) = 1.5
This is satisfied only by Graph B.
Hence answer is graph B.
When x tends to -infinity y
Find the length of a line segment with endpoints of 19 and –39. A. –58 B. –20 C. 20 D. 58
Answer:
Option D, 58
Step-by-step explanation:
Line segment having end points are 19 and -39
So total length of line segments having end points of 19 and (-39) = distance from origin to one end at (19) + distance of another end from origin
= 19 + 39
= 58
Option D, 58 is the answer.
Line GJ is tangent to point A at point G.
If AG = 9 and GJ = 12, find AJ.
Please help a brother out! Thank you!
they are saying x = 3 so you would use the middle equation
so -4x becomes -4(3)
-4 * 3 =-12
I don't understand this at all please help me
4y-y +11 = 38
4y -y = 3y
3y + 11 = 38
3y = 27
y = 27/3 =9
y = 9
answer is 9
The radius of the earth is approximately 3960 miles find the approximate surface area to volume ratio of the earth
If c is a real number and if 2+i is a solution of the equation x^2-4x+c, what is the value of c
Molly hikes 1/6 mile every day.
To hike a total of 11/6 miles, she would have to hike for____ days. To hike a total of 1/3 of a mile, she would have to hike for____ days.
she hikes 1/6 a day, to get 11/6 , she would have to hike 11 days
to hike 1/3 of a mile
1/3 / 1/6 = 1/3 * 6/1 = 6/3 = 2
so she would have to hike 2 days
Answer:
11 days and 2 days
Step-by-step explanation:
Molly hikes every day = [tex]\frac{1}{6}[/tex] miles
She would take days to hike total [tex]\frac{11}{6}[/tex] miles = [tex]\frac{\frac{11}{6} }{\frac{1}{6} }[/tex]
= [tex]\frac{11}{6}[/tex] × [tex]\frac{6}{1}[/tex] = 11 days.
To hike a total [tex]\frac{1}{3}[/tex] of a mile she would have to hike = [tex]\frac{\frac{1}{3} }{\frac{1}{6} }[/tex]
[tex]\frac{1}{3}[/tex] × [tex]\frac{6}{1}[/tex] = 2 days
To hike a total of [tex]\frac{11}{6}[/tex], she would have to hike for 11 days. To hike a total of [tex]\frac{1}{3}[/tex] of a mile, she would have to hike for 2 days
Identify the polynomial written in ascending order. 8x3+ 2x2− 6x − 11 2x2− 11 + 8x3− 6x −6x + 8x3− 11 + 2x2 −11 − 6x + 2x2+ 8x3
The answer is -11 - 6x + 2x^2 + 8x^3 <==
The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for h(x). (2 points)
Part A:
The first thing of completing the square is writing the
expression
as
which expands to
.
We have the first two terms exactly alike with the function
we start with:
and
but we need to add/subtract from the last term, 49, to
obtain 41.
So, the second step is to subtract -8 from the expression
The function in finalizing the square form is
Part B:
The vertex is acquired by equating the expression in the
bracket from part A to zero
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a
U-shape.
A quadratic function
can either make U-shape or ∩-shape depends on the
value of the constant
that goes with
. When
is (+), the curve is U-shape. When
(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will go through the vertex,
hence the symmetry line is
This function is shown in the diagram below
Answer:
Part A: The vertex form is h(x) = (x+7)^2 - 8 .
Part B: The vertex is a minimum. The vertex is (-7,-8).
Part C: The axis of symmetry is x=-7. (axis of symmetry is the x value of the vertex)
Step-by-step explanation:
This video will help you understand how I got the function into vertex form.
Search: How do you convert from standard form to vertex form of a quadratic Brian McLogan
This will help you find the vertex
Search: Finding the vertex of a parabola in standard form khan academy
A small class has 10 students, 5 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a girl and the second will be a boy? Write your answer as a fraction in simplest form.
Answer:
The required probability is 5/18.
Step-by-step explanation:
Total number of total students = 10
Number of girls = 5
Number of boys = 5
Formula for probability:
[tex]Probability=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]
The probability that the first student chosen will be a girl = [tex]\frac{5}{10}=\frac{1}{2}[/tex]
After selecting 1 student, the total number of student is
[tex]10-1=9[/tex]
The probability that the second student chosen will be a boy = [tex]\frac{5}{9}[/tex]
The probability that the first student chosen will be a girl and the second will be a boy is
[tex]P=\frac{1}{2}\times \frac{5}{9}[/tex]
[tex]P=\frac{5}{18}[/tex]
Therefore the required probability is 5/18.
All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is: P(x) = x - 0.1x P(x) = 0.9x The function that gives the price, C, if only a $150 coupon is used is: C(x) = x - 150 Choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon
We are given the functions:
P (x) = 0.9 x
C (x) = x – 150
We can generate two composition functions from the given two functions in the form of:
P [C (x)] and C [P (x)]
Since the problem states that we are to find for the final price after a 10% discount is followed by a $150 coupon then we should find for:
C [P (x)]
The value of C [P (x)] can obtained by plugging in the value of P (x) into x in the equation of C (x), therefore:
C [P (x)] = [0.9 x] – 150
C [P (x)] = 0.9 x – 150 (ANSWER)
Answer:
A On edge 2020!
Step-by-step explanation:
Have an amazing day :3
Analyze the diagram below and answer the question that follows.
Which of the following best describes triangle GFH?
A.
isosceles triangle
B.
acute triangle
C.
scalene triangle
D.
right triangle
A rectangle is 3 times as long as it is wide. The perimeter is 60cm. Find the dimensions of the rectangle.
The population of a town in 2000 was 430. The population is increasing at a rate of 0.9% every year. What will be the projected population of the town in 2010? Round your answer to the nearest whole number.
options are 440,450,460,470
What is the value of the rational expression 2x-1/x+5 when x = 0?
The value of the rational expression of equation is A = -1/5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( 2x - 1 ) / ( x + 5 )
when x = 0
Substituting the values in the equation , we get
A = ( 2 ( 0 ) -1 ) / ( 0 + 5 )
On simplifying , we get
A = -1/5
Hence , the equation is solved and A = -1/5 when x = 0
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